find the reflection of a geometric object in a point, in a line, or in a plane - Maple Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Geometry : 3-D Euclidean : Transformations : geom3d/reflection

geom3d[reflection] - find the reflection of a geometric object in a point, in a line, or in a plane

Calling Sequence

reflection(Q, P, c)

Parameters

Q

-

the name of the object to be created

P

-

geometric object

c

-

point, line, or plane

Description

• 

In reflection in a point, each point P of the set S of all points of unextended space is carried into the point P1 of S such that PP1 is bisected by a fixed point O of space.

• 

In reflection in a line, each point P of S is carried into the point P1 of S such that PP1 is perpendicularly bisected by a fixed line l of space.

• 

In reflection in a plane, each point P of S is carried into the point P1 of S such that PP1 is perpendicularly bisected by a fixed plane p of space.

• 

For a detailed description of the object created Q, use the routine detail (i.e., detail(Q))

• 

The command with(geom3d,reflection) allows the use of the abbreviated form of this command.

Examples

with(geom3d):

Define the plane oxy.

plane(oxy,[point(C,0,0,0),point(X,1,0,0),point(Y,0,1,0)]):

Define the sphere with center (1,1,1) and radius 2.

sphere(s,[point(o,1,1,1),2]);

s

(1)

Find the reflection of the sphere s in the plane oxy.

reflection(s1,s,oxy);

s1

(2)

detail(s1);

Warning, assume that the name of the axes are _x, _y and _z

name of the objects1form of the objectsphere3dname of the centercenter_s1_1coordinates of the center1,1,−1radius of the sphere2surface area of the sphere16πvolume of the sphere32π3equation of the sphere_x2+_y2+_z22_x2_y+2_z1=0

(3)

Check that s and s2, the reflection of s1, are the same.

reflection(s2,s1,oxy);

s2

(4)

AreDistinct(s,s2);

false

(5)

Plot the sphere, its reflection and the plane.

draw([s,s1,oxy],style=patch,lightmodel=light4);

See Also

geom3d[objects], geom3d[transformation]


Download Help Document

Was this information helpful?



Please add your Comment (Optional)
E-mail Address (Optional)
What is ? This question helps us to combat spam